< Calc II

Math 200

Multivariate Calculus

Course Materials

Rectangular Coordinates

Vectors

Dot Product and Projections

Cross Product

Parametric Equations of Lines

Planes

Vector-Valued Functions

Quadric Surfaces

Functions of Several Variables

Paritial Derivatives

Chain Rule

Directional Derivative

Tagent Planes and Normal Lines

Local Linear Approximation

Relative and Absolute Extrema

Double Integrals

Double Integrals with Polar Coordinates

Spherical and Cylindrical Coordinates

Triple Integrals

Jacobian and Change of Variables

Misc Examples



Resources

Paul Dawkins' Online Notes are an incredible resource that function as an interactive online textbook. These notes are available as textbooks to download in PDF format. I highly suggest using these in addition to my lecture notes and any other resources you find useful. Our calculus II course begins at the end of his Calculus II book and continues into his Calculus III book - you should be able to identify the appropriate sections by their titles.

You may find Geogebra's 3D Graphing Calculator for visualizing vectors, planes, surfaces etc. Here's how you can plot a few basic things:

  • Points: Just name a point, e.g.,
                  
                    A = (1,2,3)
                  
  • Vectors: You can find the vector connecting two points like this
                    
                      v = vector((1,2,3),(-4,-5,-6))
                    
                  
    Or get a vector in standard position by inputing a single point:
                    
                      v = vector((1,2,3))